Retarder films, sometimes also referred to as retarder plates, are known. A retarder film is constructed such that when normally incident unpolarized light passes through the film, one linear polarization state is delayed or “retarded” relative to an orthogonal linear polarization state. Light of the delayed polarization state is said to be polarized along an in-plane axis of the film referred to as the “slow axis”, and light of the other polarization state is said to be polarized along an orthogonal in-plane “fast axis”. Retarder films are tailored to provide a desired amount of delay or “retardation”, and the retardation may be measured or specified in terms of a fraction of a design wavelength of light. For example, a quarter-wave retarder causes light polarized along the slow axis to be one-fourth of a wavelength out of phase (and delayed) with respect to light polarized along the fast axis. Likewise, a half-wave retarder causes light polarized along the slow axis to be one-half of a wavelength out of phase (and delayed) with respect to light polarized along the fast axis. In these cases, the referenced “wavelength” may be a wavelength in the middle of the visible spectrum, e.g., 560 nm. Retardation may alternatively be measured in terms of the physical or optical distance that the wavefront of the delayed polarization lags behind the wavefront of the other polarization as light of the two polarization states emerge from the retarder film. (The optical distance is the physical distance multiplied by the applicable refractive index.) For the quarter-wave and half-wave examples just mentioned, the retardations are 140 nm (=560/4) and 280 nm (=560/2), respectively.
A retarder film can be designed to have specified relationships between its refractive indices along principal mutually perpendicular x-, y-, and z-axes, where the x- and y-axes are assumed to lie in the plane of the film, and the z-axis is assumed to be perpendicular to the film plane and parallel to a thickness axis of the film. The retarder film can be characterized in terms of its refractive indices along these principal axes. In this regard, we can refer to nx, ny, and nz as the refractive index of the retarder film for light whose electric field vibrates parallel to the x, y, and z axes, respectively. If nx, ny, and nz are all equal or substantially equal to each other, then the film is substantially isotropic, and no significant retardation occurs. In this isotropic case, the film functions as a window film, which does not delay or retard any polarization state relative to any other polarization state, rather than a retarder film. In other cases, the film may be uniaxially birefringent, which means that two of the principal refractive indices nx, ny, nz are equal or substantially equal to each other, and the remaining refractive index is significantly different from the other two. The two refractive indices that are substantially equal are referred to as the ordinary refractive index, and the other refractive index is referred to as the extraordinary refractive index. When one of the in-plane refractive indices (nx or ny) is equal or substantially equal to nz, and the remaining in-plane refractive index (ny or nx respectively) is substantially different, the uniaxially birefringent film is referred to as an “a-plate” retarder film. On the other hand, when the two in-plane refractive indices nx and ny are equal or substantially equal to each other, and nz is substantially different, the uniaxially birefringent film is referred to as a “c-plate” retarder film. As a consequence of these refractive index relationships, a c-plate retarder film provides no significant retardation for light that is normally incident on the film, but does provide retardation for light that is obliquely incident on the film. An a-plate retarder film, in contrast, provides retardation both for normally incident light and obliquely incident light.
In still other cases, the film may be biaxially birefringent, which means that all three principal refractive indices are significantly different from each other. A biaxially birefringent retarder film provides retardation both for normally incident light and obliquely incident light.